Write the absolute value inequality in the form x−b ≤c or x−b ≥c that has the solution set −1≤x≤3.

The solution set of | x - 1 | ≤ 2 is -1 ≤ x ≤ 3, as required.

What is inequality?

A connection between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. The inequality can be resolved by adding the same amount to each side, subtracting the same amount from each side, multiplying or dividing each side by the same positive integer, and more. If you multiply or divide either side by a negative value, you must flip the inequality sign.

To write the absolute value inequality in the form x−b ≤c or x−b ≥c, we need to identify the midpoint between the lower and upper bounds of the solution set.

The midpoint is (3 - 1)/2 = 1.

Then, we can write the absolute value inequality as:

| x - 1 | ≤ 2

To verify that this inequality has the solution set -1 ≤ x ≤ 3, we can solve it as follows:

If x - 1 ≥ 0, then | x - 1 | = x - 1, and we have:

x - 1 ≤ 2

x ≤ 3

If x - 1 < 0, then | x - 1 | = - (x - 1), and we have:

(x - 1) ≤ 2

x - 1 ≥ -2

x ≥ -1

Therefore, | x - 1 | ≤ 2.

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Answer:

|x-1| < 2

Step-by-step explanation:

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